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3D i Distribution Visualization

3D i Distribution Visualization
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2015-06-27 06:32
VectorFunctionCoordinate GeometrySolid GeometryCalculus
In collections Complex Math
This example demonstrates how to construct a three-dimensional distribution for the variable i. Key math concepts include 3D space, distribution functions, vectors, and coordinate geometry. Construction highlights involve using GeoGebra commands like Vector, Angle, Point, Segment, Polygon, Intersect, and Integral, as outlined in the summary. Suitable for high school and above, focusing on 3D visualization and integral applications in complex functions.

GeoGebra Commands & Parameters

  1. Vector((0, 1.16)) → u
  2. Vector((1.16, 0)) → v_1
  3. Angle(b, a) → α
  4. Angle(a, b) → β
  5. Angle(a, b) → γ
  6. Angle(w, a) → δ
  7. Point(w) → A
  8. Point(b) → B
  9. Segment(A, B) → d
  10. Point(a) → C
  11. Segment(A, C) → p
  12. Point(w) → D
  13. Segment(A, D) → f
  14. Angle(C, A, B) → ε
  15. Angle(C, A, D) → ζ
  16. Polygon(A, C, D, B) → poly1, a_1, c_1, d_1, b_1
  17. Point(w) → E
  18. Point(a) → F
  19. Segment(F, E) → g
  20. Point(b) → G
  21. Segment(G, E) → h
  22. Intersect(d_1, b_1) → H
  23. Intersect(c_1, d_1) → I
  24. Intersect(a_1, c_1) → J
  25. Polygon(H, I, J, F, E, G) → poly2, h_1, i, j, f_1, e_1, g_1
  26. Point(p_1) → K
  27. Vector(A, K) → k
  28. Segment(A, F) → l_2
  29. Segment(A, K) → m
  30. Angle(C, A, K) → η
  31. Segment(A, E) → n
  32. Angle(K, A, E) → θ
  33. Point(s) → L
  34. Polygon(A, L, G) → poly3, g_2, a_2, l_1
  35. Vector((0, 0), (1.16, 1.16)) → q
  36. Point(b_1) → M
  37. Segment(A, M) → l
  38. Point(q) → N
  39. Segment(A, N) → i_1
  40. Angle(c_1, b_1) → ι
  41. Angle(N, A, B) → κ
  42. Integral(r_1, -10, 10) → v
  43. Point(b) → Q
  44. Point(w) → S
  45. Point(r_1) → W
  46. Polygon(Q, S, W, A) → poly4, q_2, s_1, w_1, a_3
  47. Polygon(A, Z, T) → poly6, t_2, a_5, z_1
  48. Point(b) → A_1
  49. Point(k) → B_1
  50. Point(r_1) → C_1
  51. Point(r_1) → D_1
  52. Polygon(C_1, B_1, A_1, D_1) → poly5, c_2, b_2, a_4, d_2
  53. Segment(W, B_1) → o
  54. Point(d_2) → E_1
  55. Point(b_2) → F_1
  56. Intersect(b_2, a_4) → G_1
  57. Polygon(E_1, F_1, G_1, A) → poly7, e_2, f_2, g_3, a_6
  58. Point(q_2) → I_1
  59. Point(d_2) → H_1
  60. Polygon(H_1, A, I_1) → poly8, i_2, h_2, a_7

AI Drawing Prompt Reference

Visualize a 3D distribution for the variable i, highlighting key mathematical concepts like distribution functions, vectors, and coordinate geometry. Start by constructing two vectors u and v_1, then use angles α, β, γ, δ, and points A, B, C, D, E, F, G, H, I, J, K, L, M, N, Q, S, W, Z, T to create complex geometric structures through line segments, polygons, and integrals, showcasing the shape of the distribution function and integral applications.
The prompt above was compiled from the original drawing commands and is for reference only.